Jenny Jones is not going to be London's next mayor, but that doesn't mean casting a vote for her would be wasted. The joy of the supplementary vote system (SV) is that, like its longer relative the alternative vote system, it enables you to mark crosses on ballot papers in accordance with the different things your heart and your head might be telling you.

Londoners get not one but two votes for mayor - a first and a second preference. An awful lot of people - including, it seems, some very august commentators - are unaware of this. A lot of those who are aware might not have figured out the implications in terms of what the opinion polls are telling us about the possible outcome of the mayoral race.

It is absolutely plain that either Boris Johnson or Ken Livingstone is going to win - they are miles ahead of the rest of the field - but if you like Jenny's policies best, you can still give her your first preference (the choice of the heart) and bestow your second preference on Boris or Ken depending on which of the two you like most or dislike least (the choice of the head).

In this way you can vote according to principle and tactically at the same time, should you so wish - simultaneously honouring your electoral conscience and having a possibly crucial impact on who actually wins. Under SV it's almost certain that second preference votes for either of the two frontrunners will, in the end, be of equal value to them as first preferences. That is because neither frontrunner is on course to win the more than 50% of first preference votes he'd need in order to make second preferences irrelevant.

The same "heart" option exists if you like Brian Paddick best, or Siobhan Benita or anyone else who isn't Boris or Ken. So why might your heart go Green? In my case, there are three main reasons.

One: Transport polices that recognise that economic efficiency and environmental quality of life can and should be entirely consistent goals in modern cities. I don't share the apparent Green aversion to fossil fuelled motor vehicles, but I do think that our capitalist metropolis would function both more profitably and more pleasantly if many fewer clogged London's roads. That's why I like their proposal for a London-wide pay-as-you-go road-pricing system and accompanying pledge that the cost of travelling by public transport should always be lower than going by car.

Two: A good vote yield for Jenny would further establish Green Party politics in the London politics mainstream. As London Assembly members, she and her colleague Darren Johnson have brought variety, industry, persistence and - most importantly - some good influence to bear on mayoral policy, particularly when Ken was mayor.

Three: My unscientific judgement is that the Guardian's crowdsourced manifesto for a model mayor overlaps to a greater degree with Jenny's than with that of any other candidate. Something else they have in common is a high degree of idealism, though not to the point of outright impracticality.

This is a good thing. Yes, the Greens can afford to dream big dreams because they know their own supporters do the same and because they also know that no amount of pragmatic positioning will win them City Hall anyway. But we need idealism. When I read the Green manifesto, an idealistic kind of London forms in my mind - a sort of hybrid of small-is-beautiful socialism, peaceful anarchism and humane thrift. Yes, I know it's a long way off, but where the heart is concerned why not aim high?